$\dfrac{d}{dx}\left(x^{-9}\right)=$
Solution: The derivative can be found using the power rule : $\dfrac{d}{dx}(x^n)=n\cdot x^{n-1}$ (Remember that this applies even when $n$ is a negative number.) $\begin{aligned} &\phantom{=}\dfrac{d}{dx}\left(x^{-9}\right) \\\\ &=-9x^{-9-1} \gray{\text{The power rule}} \\\\ &=-9x^{-10} \end{aligned}$ In conclusion, we found that $\dfrac{d}{dx}\left(x^{-9}\right)=-9x^{-10}$. This can also be written as $-\dfrac{9}{x^{10}}$ (all equivalent forms are accepted).